Details

simplify6.4m (42.0%)

sample3.3m (21.6%)

Algorithm
61×intervals
Results
42.4s252518×body80valid
40.0s29536×body1280valid
28.4s160829×body80nan
19.6s20035×body640valid
17.4s8657×body2560valid
10.2s3467×body5120valid
6.5s9925×body320valid
4.6s8868×body160valid
1.1s814×body10240exit
345.0ms620×body1280nan
211.0ms598×body640nan
196.0ms8256×pre80true
155.0ms401×body320nan
34.0ms190×body160nan

series2.7m (17.4%)

Calls

434 calls:

7.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
7.4s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
7.3s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
7.2s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
2.5s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))

prune1.7m (11.1%)

rewrite49.7s (5.4%)

Algorithm
116×rewrite-expression-head
Calls

434 calls:

9.2s
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
3.6s
(/ (+ (pow 1.0 3) (pow (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)) 3)) (fma 1.0 1.0 (* (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)) (- (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)) 1.0))))
3.1s
(- (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)) 1.0)
1.2s
(/ (/ 2.0 (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))
1.1s
(/ (/ 2.0 (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (* (/ (pow (cbrt t) 3.0) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))
Rules
45497×add-exp-log
31597×prod-exp
19788×pow-exp
16320×div-exp
10088×pow-to-exp
8705×times-frac
6688×add-sqr-sqrt
6212×*-un-lft-identity
5132×add-cube-cbrt
4415×sqrt-prod
2936×add-cbrt-cube
1922×1-exp rec-exp
1651×unpow-prod-down
1252×associate-*l*
1233×cbrt-unprod
1088×pow1
1050×cbrt-prod
808×associate-*r*
772×difference-of-squares
683×cbrt-undiv
654×sqr-pow
647×prod-diff
552×associate-/l*
507×add-log-exp
475×associate-/r* div-inv
436×log1p-expm1-u expm1-log1p-u
419×associate-*l/
392×pow-unpow
383×associate-*r/
342×distribute-lft-out--
340×cube-prod
334×associate-/r/
332×pow-prod-down
305×distribute-lft-out
284×frac-times
227×distribute-rgt-neg-in
193×distribute-lft-neg-in
188×unswap-sqr
171×fma-def
166×tan-quot
163×flip3-- flip--
157×distribute-rgt-in distribute-lft-in
127×sqrt-div
124×exp-sum
123×*-commutative
106×clear-num frac-2neg
104×cos-sum
80×sin-sum swap-sqr
73×sqrt-pow1
67×pow1/3
64×sub-neg
57×rem-sqrt-square
51×pow1/2
47×associate-/l/ pow-pow
45×associate--l+
37×fma-neg
36×flip-+ flip3-+ frac-sub
35×pow-sub exp-prod
34×div-sub
30×cbrt-div
28×neg-sub0
27×unpow2
24×fma-udef
22×pow-neg unpow-prod-up associate--r+ sum-log
20×neg-mul-1
19×unpow3 cube-mult
17×+-commutative
15×diff-log
14×pow-flip
12×hypot-def
10×pow-prod-up
9×frac-add
8×un-div-inv inv-pow pow-sqr
7×pow-plus distribute-neg-frac
5×rem-cube-cbrt pow2 sum-cubes log-pow acos-asin
4×cube-div exp-diff hypot-udef log-prod
3×log1p-udef log1p-expm1 expm1-log1p neg-log expm1-udef associate-+l-
2×associate-+l+ pow-div cos-diff unsub-neg distribute-frac-neg associate-+r- asin-acos rem-cbrt-cube
1×rem-exp-log expm1-def associate--l- difference-of-sqr-1 associate--r- mul0 rem-log-exp sin-diff

regimes14.9s (1.6%)

Accuracy

Total 36.5b remaining (18.1%)

Threshold costs 4.6b (2.3%)

9.4b6.5%Toniolo and Linder, Equation (13)
5.6b76.5%Toniolo and Linder, Equation (7)
4.9b-7.9%Henrywood and Agarwal, Equation (12)
3.9b52.6%Toniolo and Linder, Equation (10-)
3.1b30.8%Toniolo and Linder, Equation (10+)

localize4.3s (0.5%)

bsearch3.0s (0.3%)

end0.0ms (0.0%)